The claim "No human lives forever" is not falsifiable since one would have to observe a human living forever to falsify that claim.
Thinking on similar lines, even if the coin is fair, it can produce a arbitrarily long(finite) sequence of continuous heads with finite but small probability.
So if you were to determine whether a coin is not fair, you will have to toss it to eternity to be sure.
The assumption here is that it is not possible to determine the fairness just by looking at the physical properties alone.
Does falsifiability require the process of falsification be finished in finite time?